Abstract
In the present study, standard Tikhonov regularization (STR) Technique and the subspace regularization (SR) method have been applied to remove the additive EEG noise on average auditory-evoked potential (EP) signals. In methodological manner, the difference between these methods is the formation of regularization matrices which are used to solve the weighted problem of EP estimation. Those methods are compared to ensemble averaging (EA) with respect to signal-to-noise-ratio (SNR) improvement in experimental studies, simulations and pseudo-simulations. The results of tests no superiority of the SR in comparison to STR has been observed. In addition, the STR is found to be less computational complex. Moreover, results support the theoretical fact that the STR was introduced to be optimum for smooth solutions whereas the SR allows sharp variations in solutions. Thus, the STR is found to be more useful in removing the noise with the average signal remaining.
This is a preview of subscription content, log in via an institution to check access.
References
Aydın S (2008) Comparison of basic linear filters in extracting auditory evoked potentials. Turk J Elec Eng 16:72–728
Bronzino JD (2000) The biomedical engineering handbook. CRC Press
Daucbechies I (1992) Ten lectures on wavelets. SIAM
Davila CE, Srebro R (2000) Subspace averaging of steady-state visual evoked potentials. IEEE Trans BME 47:720–728
Furst M, Blau A (1991) Optimal a posteriori time domain filter for average evoked potentials. IEEE Trans BME 38:827–833
Gupta L, Molfese DL (1996) Nonlinear alignment and averaging for estimating the evoked potential. IEEE Trans BME 43:34–356
Hansen PC (1994) Regularization tools, numerical algorithms
Karjalainen PA, Kaipio JP (1999) Subspace regularization method for the single-trial estimation of evoked potential. IEEE Trans BME 46:849–859
Qiu W, Fung SM, Chan HY, et al (2002) Adaptive filtering of evoked potentials with radial basis function neural network pre-filter. IEEE Trans BME 49:225–231
Quiroga RQ, Garcia H (2003) Single trial event related potentials with wavelet de-noising. EEG Clin Neuroph 114:376–390
Shooshtari P, Mohamadi G et al (2007) Removing ocular artifacts from EEG signals using adaptive filtering and ARMAX modeling. Med Biol Eng Comput 45(5):495–503
Tikhonov AN, Arsenin VY (1977) Solution of ill-posed problems. Winston and Sons
Turetsky BI, Raz J (1988) Noise and signal power and their effects on evoked potential estimation. Clin Neuroph 71:310–318
Vauhkonen M (1998) Tikhonov regularization and prior information in electrical impedance tomography. IEEE Trans Med Imag 17:285–293
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Aydın, S. Tikhonov regularized solutions for improvement of signal-to-noise ratio in case of auditory-evoked potentials. Med Biol Eng Comput 46, 1051–1056 (2008). https://doi.org/10.1007/s11517-008-0385-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11517-008-0385-0